Question

Simplify the following:
$\sqrt{72} - \sqrt{50} + \sqrt{128}$
​

Answer 1

Answer :-

To solve such question, we first need to prime factorize the numbers. After prime factorization, we need to form pair of similar prime numbers and then we will take it out of the square root. After that we will add or subtract only the like terms ( which have same number in square roots ) and we can get our final answer.

$\sf\implies\sqrt{72} - \sqrt{50} + \sqrt{128}$

• Prime factorization of 72 = 2 × 2 × 2 × 3 × 3

• Prime factorization of 50 = 2 × 5 × 5

• Prime factorization of 128 = 2 × 2 × 2 × 2 × 2 × 2 × 2

$\sf\implies\sqrt{2 \times 2 \times 2 \times 3 \times 3} - \sqrt{5 \times 5 \times 2 } + \sqrt{2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2}$

$\sf\implies2 \times 3\sqrt2 - 5\sqrt2 + 2\times2\times 2\sqrt2$

$\sf\implies6\sqrt2 - 5\sqrt2 + 8\sqrt2$

$\sf\implies1\sqrt2 + 8\sqrt2$

$\sf\implies9\sqrt2$

$\boxed{\sf\sqrt{72} - \sqrt{50} + \sqrt{128} = 9\sqrt2}$